Generalized Newtonian fluid, definition

The definition (2 85) is a purely mechanical definition of pressure for a moving fluid, and nothing is implied directly of the connection for a moving fluid between p and the ordinary static or thermodynamic pressure p. Although the connection between p and p can always be stated once the constitutive equation for T is given, one would not necessarily expect the relationship to be simple for all fluids because thermodynamics refers to equilibrium conditions, whereas the elements of a fluid in motion are clearly not in thermodynamic equilibrium. Applying the definition (2-85) to the general Newtonian constitutive model, (2-80), we find... 

Here the absolute value of the velocity gradient is called the shear rate. For a newtonian fluid it is known that in this simple shear flow only the shear stress zxy is nonzero. However, it is possible that all six independent components of the stress tensor may be nonzero for a non-newtonian fluid according to its definition. For simple shearing flow of an isotropic fluid it can be proven [6] that the total stress tensor can have the general form... 

The Flux Expressions. We begin with the relations between the fluxes and gradients, which serve to define the transport properties. For viscosity the earliest definition was that of Newton (I) in 1687 however about a century and a half elapsed before the most general linear expression for the stress tensor of a Newtonian fluid was developed as a result of the researches by Navier (2), Cauchy (3), Poisson (4), de St. Venant (5), and Stokes (6). For the thermal conductivity of a pure, isotropic material, the linear relationship between heat flux and temperature gradient was proposed by Fourier (7) in 1822. For the difiiisivity in a binary mixture at constant temperature and pressure, the linear relationship between mass flux and concentration gradient was suggested by Pick (8) in 1855, by analogy with thermal conduction. Thus by the mid 1800 s the transport properties in simple systems had been defined. 

ASTM D.3835-95a [21] fulfils the same purpose and is very generally the same as ISO 11443. Unfortunately the standards differ a lot in detail, not so much in quantitative data but mainly in that one standard describes details that arc left out of the other. Thus under definitions the ISO standard defines Newtonian and non-Newtonian fluids and the ASTM standard does not. The converse applies for delay lime. ... 

As shown in Eqn. (6), the drag coefficient of a cylindrical fiber imder cross flow condition is a function of the Reynolds Number, which is generally expressed as Re = pUp,hd/p (i.e. the ratio of inertial force to viscous force). This definition holds true for Newtonian fluids, where shear stress < shear rate. However, the fluids that are often utilized in fiber sweep applications are non-Newtonian. Hence, the Reynolds Number must be redefined using the apparent viscosity function as Re = pUp>d/papp. The viscosity for Newtonian fluids is independent of the shear rate. However, for non-Newtonian fluids, the apparent viscosity varies with shear rate. Applying the Yield Power Law (YPL) rheology model, the apparent viscosity is expressed as ... 

Newtonian constitutive equation, (2 80), that the normal component of the surface force or stress acting on a fluid element at a point will generally have different values depending on the orientation of the surface. Nevertheless, it is often useful to have available a scalar quantity for a moving fluid that is analogous to static pressure in the sense that it is a measure of the local intensity of squeezing of a fluid element at the point of interest. Thus it is common practice to introduce a mechanical definition of pressure in a moving fluid as... 

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